The deformed fish (I’m pretty sure it was born like that) looks oddly naked. Fortunately forward locomotion is mostly the job of the tail (which is itself a fin, the caudal fin). So I have to imagine that a fish would be OK without any other fins at all, though it would find steering difficult. It might crash into the walls of the aquarium a lot. My naked goldfish doesn’t do that.

Incidentally, that it swims with no trouble, rather than constantly struggling to figure out how, suggests what scientists, schoolchildren, and the Mythbusters have proved many times over, that goldfish have a long-term memory. It lasts at least a few months!